All categories

3 years ago

When is a polynomial factored completely?

Mathematics

1 answer:

Jet001 [13]3 years ago

8 0

Answer:

A polynomial is factored completely when nothing else in the expression can be factored

Example:

x^2+3x-4 completely factored looks like (x+4)(x-1)

You might be interested in

454.12kg ;3 significant digits

Westkost [7]

You can write it as 454 kg in 3 significant digits.

4 0

3 years ago

Please don't answer wrong.

Tamiku [17]

Answer:

<u />

<u>Equation of a circle</u>

$(x-a)^2+(y-b)^2=r^2$

where:

(a, b) is the center
r is the radius

Given equation: $x^2+y^2=6.25$

Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:

center = (0, 0)
radius = $\sqrt{6.25}=2.5$

To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.

Given equation: $x+y=1.5$

Rearrange the given equation to make y the subject: $y=-x+1.5$

Find two points on the line:

$x=-2 \implies -(-2)+1.5=3.5\implies (-2,3.5)$

$x=2 \implies -(2)+1.5\implies-0.5\implies (2,-0.5)$

Plot the found points and draw a straight line through them.

The <u>points of intersection</u> of the circle and the straight line are the solutions to the equation.

To solve this algebraically, substitute $y=-x+1.5$ into the equation of the circle to create a quadratic:

$\implies x^2+(-x+1.5)^2=6.25$

$\implies x^2+x^2-3x+2.25=6.25$

$\implies 2x^2-3x-4=0$

Now use the quadratic formula to solve for x:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

$\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(2)(-4)}}{2(2)}$

$\implies x=\dfrac{3 \pm \sqrt{41}}{4}$

To find the coordinates of the points of intersection, substitute the found values of x into $y=-x+1.5$

$\implies y=-\left(\dfrac{3 + \sqrt{41}}{4}\right)+1.5=\dfrac{3-\sqrt{41}}{4}$

$\implies y=-\left(\dfrac{3 - \sqrt{41}}{4}\right)+1.5=\dfrac{3+\sqrt{41}}{4}$

Therefore, the two points of intersection are:

$\left(\dfrac{3 + \sqrt{41}}{4},\dfrac{3-\sqrt{41}}{4}\right) \textsf{ and }\left(\dfrac{3 - \sqrt{41}}{4},\dfrac{3+\sqrt{41}}{4}\right)$

Or as decimals to 2 d.p.:

(2.35, -0.85) and (-0.85, 2.35)

6 0

2 years ago

Given that f(x)=3x+1 and g(x)=4x+2/4, solve for g(f(0))

maksim [4K]

$f(x)=3x+1\\\\g(x)=\dfrac{4x+2}{4}\\\\f(0)=3\cdot0+1=0+1=1\\\\g(f(0))=g(1)=\dfrac{4\cdot1+2}{4}=\dfrac{4+2}{4}=\dfrac{6}{4}=\dfrac{6:2}{4:2}=\dfrac{3}{2}=1.5$

7 0

3 years ago

How to solve quadratic inequalities.

Digiron [165]

Find all the zeros of the polynomial, and arrange the zeros in increasing order. ...

Plot those numbers on the number line as open or closed points based upon the original inequality symbol.

Choose a test value in each interval to see if the interval satisfies the inequality or not.

6 0

2 years ago

Residents of the 50 most populous metropolitan statistical areas in the United States listed ____ as one of cities where they fe

Nuetrik [128]

Answer:

fifty dollors a night

100/2=50

8 0

2 years ago